Lesson Plan for Online Lecture on Forces

I am using this post as a way to document my brief plans for tomorrow’s Google Meet lecture with the LOA students as well as to park the links to the resources and tools that I intend to use for easy retrieval.

Google Meet URL: https://meet.google.com/vyz-btyv-xks

Instruction Objectives:

  1. apply the principle of moments to new situations or to solve related problems.
  2. show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium.
  3. use a vector triangle to represent forces in equilibrium.
  4. *derive, from the definitions of pressure and density, the equation 𝑝=𝜌𝑔ℎ.
  5. *solve problems using the equation 𝑝=𝜌𝑔ℎ.
  6. *show an understanding of the origin of the force of upthrust acting on a body in a fluid.

Activity 1: Find CG of ruler demonstration

Having shown them the demonstration last week, I will explain the reason why one can find the CG this way:

  1. As I move the fingers inward, there is friction between the ruler and my finger. This friction depends on the normal contact force as $f=\mu N$.
  2. Drawing the free-body diagram of the ruler, there are two normal contact forces acting on the ruler by my fingers. The sum of these two upward forces must be equal to the weight of the ruler. These forces vary depending on their distance from the CG. Taking moments about the centre of gravity, $$N_1\times d_1=N_2 \times d_2$$
  3. The finger that is nearer to the CG will always have a larger normal contact force and hence, more friction. Hence, the ruler will tend to stop sliding along that finger and allow the other finger to slide nearer. When that other finger becomes closer to the CG, the ruler also stops sliding along it and tends to then slide along the first finger.
  4. This keeps repeating until both fingers reach somewhere near the CG.

Activity 2: Moments of a Force at an Angle to the line between Pivot and Point of Action.

  1. Recollection of the slides on moment of a force and torque of a couple.
  2. Give them a MCQ question to apply their learning using Nearpod’s Quiz function https://np1.nearpod.com/presentation.php?id=47032717
  3. Ask students to sketching on Nearpod’s “Draw It” slides the “perpendicular distance between axis of rotation and line of action of force” and “perpendicular distance between the lines of action of the couple” for Example 5 and 6 of the lecture notes respectively.
  4. Mention that
    1. axis of rotation is commonly known as where the pivot is
    2. perpendicular distance is also the “shortest distance”

Activity 3: Conditions for Equilibrium

  1. State the conditions for translational and rotational equilibrium
  2. Show how translation equilibrium is due to resultant force being zero using vector addition
  3. Show how rotational equilibrium is due to resultant moment about any axis being zero by equating sum of clockwise moments to sum of anticlockwise moments.
  4. Go through example 7 (2 methods: resolution of vectors and closed vector triangle)
  5. Useful tip: 3 non-parallel coplanar forces acting on a rigid body that is in equilibrium must act through the same point. Use 2006P1Q6 as example.
  6. Go through example 8. For 8(b), there are two methods: using concept that the 3 forces pass through the same point or closed triangle.

For next lecture (pressure and upthrust):

Activity 4: Hydrostatic Pressure

  1. Derive from definitions of pressure and density that $p = h\rho g$
  2. Note that this is an O-level concept.

Activity 5: Something to sink about

Get students to explain how the ketchup packet sinks and floats.

Students are likely to come up with answers related to relative density. As them to draw a free body diagram of the ketchup packet. However, we will use the concept of the forces acting on the ketchup packet such as weight and upthrust to explain later.

Activity 6: Origin of Upthrust

I designed this GeoGebra app to demonstrate that forces due to pressure at different depths are different. For a infinitesimal (extremely small) object, the forces are equal in magnitude even though they are of different directions, which is why we say pressure acts equally in all directions at a point. However, when the volume of the object increases, you can clearly see the different in magnitudes above and below the object. This gives rise to a net force that acts upwards – known as upthrust.

Free-Body Diagrams in Two-Body Motion


Students are often confused about the forces in drawing free-body diagrams, especially so when they have to consider the different parts of multiple bodies in motion.

Two-Body Motion

Let’s consider the case of a two-body problem, where, a force F is applied to push two boxes horizontally. If we were to consider the free-body diagram of the two boxes as a single system, we only need to draw it like this.

two-body

Considering both boxes as a single system

For the sake of problem solving, there is no need to draw the normal forces or weights since they cancel each other out, so the diagram can look neater. Applying Newton’s 2nd law of motion, F=(m_A+m_B) \times a, where m_A is the mass of box A, m_B is the mass of box B, F is the force applied on the system and a is the acceleration of both boxes.

You may also consider box A on its own.

DYNAMICS2

Considering box A on its own

The equation is F-F_{AB}=m_A \times a, where F_{AB} is the force exerted on box A by box B.

The third option is to consider box B on its own.

DYNAMICS3

Considering box B on its own

The equation is F_{BA}=m_B \times a, where F_{BA} is the force exerted on box B by box A. Applying Newton’s 3rd law, F_{BA}=F_{AB} in magnitude.

Never Draw Everything Together

NEVER draw the free-body diagram with all the forces and moving objects in the same diagram, like this:

wrong freebody diagram

You will not be able to decide which forces acting on which body and much less be able to form a sensible equation of motion.

Interactive

Use the following app to observe the changes in the forces considered in the 3 different scenarios. You can vary the masses of the bodies or the external force applied.

Multiple-Body Problems

For the two-body problem above, we can consider 3 different free-body diagrams.

For three bodies in motion together, we can consider up to 6 different free-body diagrams: the 3 objects independently, 2 objects at a go, and all 3 together. Find the force between any two bodies by simplifying a 3-body diagram into 2 bodies. This trick can be applied to problems with even more bodies.

Home-Based Learning Using Google Meet

I conducted an online lecture this morning using Google Meet for the students who had to stay home due to the Leave of Absence mandated by the Ministry since they had recently returned from another country during this period of the Covid-19 pandemic. I feel the need to document this as things might become bad enough that schools have to close, so it serves as a place where fellow teachers can pick up some tips on how to manage this.

The G Suite account that I used is that of my school’s, not MOE’s, because it allows me to record the session in case I need to show the session to students who did not “turn up” for the Meet. I am the G Suite admin for the school so I changed the setting to allow Google Meets to be recorded. After the session, the recorded Meet is automatically found in a G Drive folder after it has been processed in the backend. ICON’s Google Meet (part of MOE’s Google Suite service) does not allow recording.

My hardware setup is simple: just my laptop to capture my face and control the Google Meet UI and a second screen with which to show my slides. I also entered the Meet as another participant using my mobile phone as I wanted to see what my students would see for added assurance.

Google Meet is very user-friendly, with a minimalist and intuitive design that one can expect from Google (after all, that was what made it the preferred search engine in the early days of the internet). All we needed to do was to sign in to https://meet.google.com/ and start a session. You can also schedule a session on Google Calendar.

When a Meet is created, a URL is generated, which you can communicate to your students via text message or email, or through a system announcement.

When students log in, be sure to ask them to switch off their video and mute their voices so as not to cause any interference.

Note that what is shown in the presenter’s screen in Meet using the front camera of a laptop is laterally inverted as presenters generally want to see themselves as though they are looking at a mirror. So if you were to write things on a whiteboard or piece of paper, you will not be able to read the writing through your screen. However, rest assured that students can still read the writing if they are looking at you through the feed from your laptop’s front camera.

Instead, what I did was to toggle between showing my face on the camera and projecting a window or a screen.

For today’s Meet, I projected a window where my Powerpoint slides was on but did not go into slide mode (which will take up both my screens) as I wanted to be able to see the Google Meet UI at all times in order to know if anyone asked questions or raised an issue using the Chat function. This backchannel was very good as students could immediately tell me if they could see or hear me. I wanted them to be able to ask questions through that but nobody did, unfortunately.

A few times, I toggled to use the camera. Once, it was to show a simple physics demonstration which I felt added some badly needed variety.

For future sessions, I intend to project a single window with Chrome is so that I can project the slides using Google Slides in an extended mode. This will also allow me to switch to an online video with ease instead of selecting the window via the Google Meet UI, which might throw up too many options if one has many windows open (which I tend to do). I also intend to use Nearpod to gather some responses from the students.

Collision Simulation

I created this post here to bookmark some useful tools for use during my upcoming JC1 lectures on Dynamics.

This is a simulation for collisions that show the momenta before and after collisions. It requires registration after one visit.

A better choice for now could be the EJSS version (created by my ex-colleague Lawrence) which is far more detailed.

I had wanted to build one using GeoGebra and in fact, was halfway through it, but the Covid-19 pandemic has created other areas of work that now take priority.

Newton’s 3rd Law

Activity 1: Propeller Cart (Predict, Observe and Explain)

Activity 2: Untied Balloon

A balloon is filled with air and released with its mouth downwards. Explain

  1. why it moves upwards.                      
  2. why it stops rising after some time.   

Activity 3: Water Rocket

Prepopulated Free-Response Question in SLS

Now that the newest release of the Student Learning Space (SLS) is live, I was keen to try out the new features. Having heard that there is an option for prepopulated free response questions where students can draw on prefilled images, I was eager to test it.

I have made a video of the creation, student attempt and teacher feedback stages for any teacher (only for Singapore schools, though) who is keen to learn.

Two Body Problems in Dynamics

Problems involving two bodies moving together usually involve asking for the magnitude of the force between the two.

For example:

A 1.0 kg and a 2.0 kg box are touching each other. A 12 N horizontal force is applied to the 2.0 kg box in order to accelerate both boxes across the floor. Ignoring friction, determine:

(a) the acceleration of the boxes, and

(b) the force acting between the boxes.

To solve for (b) requires an understanding that the free-body diagram of the 1.0 kg box can be considered independently as only the force acting between the two boxes contributes to its acceleration since it is the only force acting on it in the horizontal direction.

This interactive app allows for students to visualise the forces acting on the boxes separately as well as a single system.

The codes for embedding into SLS:

<iframe scrolling="no" title="Two Mass Problem" src="https://www.geogebra.org/material/iframe/id/fh5pwc37/width/638/height/478/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="638px" height="478px" style="border:0px;"> </iframe>

Measuring Difference in Drop Time Using PhyPhox

In a recent class on Kinematics, I prepared a string of 4 pendulum balls, each separated about 20 cm apart and dropped them from a height. Before that, I got students to predict whether the intervals in time between drops will be constant, increasing or decreasing.

Most students are able to predict rightly that the intervals will be decreasing and explain their reasoning.

What challenged me was this: previously, we had to listen to the intervals of sound to verify the answer. I had tried using laptop software such as Audacity to record the sound before. However, I wanted students to be involved in this verification process. PhyPhox enabled that.

With each student being able to download the mobile app into their phones, all I needed to do was to ensure everyone uses the correct setting: the Audio Scope setting and to change their range to the maximum duration (500 ms). They then had to be familiar with the play and pause button so they can stop the measurement in time to see the waveform.

I then did a countdown before dropping the balls. This is an example of the graph obtained.

Through this graph, you can see that:

  1. the time interval between drops decreases as the balls dropping over a larger height had gained more velocity by the time they reach the table.
  2. the amplitude of sound increases as the balls drop with increasing velocity, therefore hitting the table with larger force.

Relationship between displacement-time and velocity-time graphs

Through this GeoGebra app, students can observe how the gradient of the displacement-time graph gives the instantaneous velocity and how the area under the velocity-time graph gives the change in displacement.

In the GeoGebra app below, you will see a displacement-time graph on the left and its corresponding velocity-time graph on the right. These graphs will be referring to the same motion occuring in a straight line. Instructions

  1. Click “Play” and observe the values of displacement and velocity change in each graph over time.
  2. Note the relationship between the gradient in the displacement-time graph and the value of velocity.
  3. Note the relationship between the area under the velocity-time graph and the value of displacement.